Preheat oven to 425°F. Line a rimmed baking sheet with parchment paper.
Pat the pork tenderloin dry with paper towels. Trim off any silver skin. Place the pork tenderloin in the center of the baking sheet.
1 pork tenderloin
In a small bowl, stir together the brown sugar, paprika, garlic powder, dried thyme, salt and pepper. Sprinkle the seasonings over all sides of the pork and gently rub into the meat. Drizzle the 2 teaspoons olive oil over the pork.
2 teaspoons brown sugar, ½ teaspoon paprika, ½ teaspoon garlic powder, ½ teaspoon dried thyme, ½ teaspoon salt, ⅛ teaspoon black pepper, 2 teaspoons olive oil
Slice the potatoes in half (unless very small) and place them in a large mixing bowl. Slice the carrots on the bias/diagonal into 1-inch pieces. Cut any pieces that are very thick in half lengthwise. Place them in the bowl with the potatoes.
1½ pounds baby potatoes, 1½ pounds whole carrots
Drizzle the olive oil over the potatoes and carrots and toss to coat. Sprinkle the fresh rosemary, salt and pepper over them and toss to evenly coat the vegetables with the seasonings. Spread the potatoes and carrots around the pork tenderloin on the baking sheet.
2 tablespoons olive oil, 1 ½ teaspoons chopped fresh rosemary*, salt and pepper
Bake for 25-35 minutes, tossing the vegetables halfway through the cook time, until an instant read thermometer inserted into the center of the pork registers at least 145° F.
Let pork rest for 5 minutes before slicing and serving it with the potatoes and carrots.